Mathematical Sciences: Microlocal Character Theory for Representations of Classical Lie Groups

数学科学：经典李群表示的微局部特征理论

• 批准号: 9204488
• 负责人: Tomasz Przebinda
• 金额: $ 3.86万
• 依托单位: University of Oklahoma Norman Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1995-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9204488&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Microlocal; Character; Theory

Przebinda will investigate distribution characters and matrix coefficients of irreducible unitary representation of classical Lie groups from the viewpoint of microlocal analysis in the context of Howe's theory of reductive dual pairs, via the Cayley transform. Use will be made of Howe's theory, microlocal analysis, and Harish-Chandra's theory of orbital integrals to construct irreducible unitary representations of classical Lie groups, attached to nilpotent coadjoint orbits. This attachment occurs on three levels: associated varieties, wave front sets, and character formulas. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics. **//

Przebinda将在Howe的约化对偶理论的背景下，通过Cayley变换，从微局域分析的角度研究经典李群的不可约么正表示的分布特征和矩阵系数。我们将利用Howe的理论、微局域分析和Harish-Chandra的轨道积分理论来构造附加在幂零余共轭轨道上的经典李群的不可约么正表示。这种依附发生在三个层面上：相关的变种、波前集合和角色公式。李群理论是以挪威数学家索菲斯·李的名字命名的，一直是20世纪数学的主要主题之一。作为利用系统固有对称性的数学工具，李群的表示理论对数学本身，特别是在分析和数论方面，以及对理论物理，特别是量子力学和基本粒子物理，都产生了深远的影响。**//